Journal ArticleDOI
Efficient and rapid numerical evaluation of the two-electron, four-center Coulomb integrals using nonlinear transformations and useful properties of Sine and Bessel functions
TLDR
In this article, an efficient approach for improving convergence of semi-infinite very oscillatory integrals, based on the nonlinear D-transformation and some useful properties of spherical Bessel, reduced Bessel and sine functions, is presented.About:
This article is published in Journal of Computational Physics.The article was published on 2002-02-01. It has received 42 citations till now. The article focuses on the topics: Slater integrals & Trigonometric integral.read more
Citations
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Journal ArticleDOI
A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem
Frederic Gibou,Ronald Fedkiw +1 more
TL;DR: This paper first describes a fourth order accurate finite difference discretization for both the Laplace equation and the heat equation with Dirichlet boundary conditions on irregular domains, then turns its focus to the Stefan problem and constructs a third order accurate method that also includes an implicit time discretizations.
Journal ArticleDOI
A numerical method for solving variable coefficient elliptic equation with interfaces
Songming Hou,Xu-Dong Liu +1 more
TL;DR: In this paper, a 2nd order accurate numerical method on non-body-fitting grids is proposed for solving the variable coefficient elliptic equation in disjoint subdomains separated by interfaces.
Journal ArticleDOI
An implicit interface boundary integral method for Poisson's equation on arbitrary domains
TL;DR: A simple formulation for constructing boundary integral methods to solve Poisson’s equation on domains with smooth boundaries defined through their signed distance function based on averaging a family of parameterizations of an integral equation defined on the boundary of the domain.
Journal ArticleDOI
An extremely efficient and rapid algorithm for numerical evaluation of three-centre nuclear attraction integrals over Slater-type functions
Lilian Berlu,Hassan Safouhi +1 more
TL;DR: In this paper, an extremely accurate and rapid algorithm for the numerical evaluation of the three-centre nuclear attraction integrals over B functions and over Slater-type functions is presented.
Journal ArticleDOI
An extremely efficient approach for accurate and rapid evaluation of three-centre two-electron Coulomb and hybrid integrals over B functions
TL;DR: In this article, Steinborn's analytical expressions of three-centre two-electron Coulomb and hybrid integrals over B functions are obtained using the Fourier transform method.
References
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Book
AB INITIO Molecular Orbital Theory
TL;DR: In this paper, the use of theoretical models as an alternative to experiment in making accurate predictions of chemical phenomena is discussed, and the formulation of theoretical molecular orbital models starting from quantum mechanics is discussed.
The Theory of Atomic Spectra
Edward U. Condon,G. H. Shortley +1 more
TL;DR: In this paper, the quantum mechanical method is applied to the theory of complex spectra and the Russell-Saunders case is used to obtain the energy levels of one-electron spectra.
Book
The Theory of Atomic Spectra
Edward U. Condon,G. H. Shortley +1 more
TL;DR: In this paper, the quantum mechanical method is applied to the theory of complex spectra and the Russell-Saunders case is used to obtain the energy levels of one-electron spectra.
Related Papers (5)
The Fourier transforms of some exponential‐type basis functions and their relevance to multicenter problems
Fourier transform of a two-center product of exponential-type orbitals. Application to one- and two-electron multicenter integrals
Extremely compact formulas for molecular two-center one-electron integrals and Coulomb integrals over Slater-type atomic orbitals
Eckhard Filter,E. Otto Steinborn +1 more